Finite element analysis for induction heating process including magnetic and thermal situations is presented. Because magnetic and thermal material properties vary with the temperature, material properties depending on temperature are considered. As the inductor moves, the solution domains corresponding to the inductor change into those of the air and the solution domains corresponding to the air change into those of the inductor. For these reasons, modeling of induction heating process is very difficult with a general purpose commercial programs. In this paper, three dimensional analysis of induction heating process for moving inductor is analyzed using moving coordinate. The skin effect is confirmed inside the steel plate in the electro-magnetic analysis. The distribution of heat generation at the initial state is different from that at the quasi-stationary state. Therefore, material properties depending on temperature must be considered. The calculated results of finite element analysis agree well with the experimental temperature results. This approach is suitable to solve magneto-thermal coupled problems.